Two important limits:
for any real number k
for all k > 0
The basic series expansions[edit | edit source]
The integral : is said to be improper if
- the interval of integration is infinite, or;
- f(x) is not defined at one or both of the end points x=a and x=b, or;
- f(x) is not defined at one or more interior points of the interval .
The area bounded by a polar curve[edit | edit source]
For the curve
r must be defined and be non-negative throughout the interval
Numerical methods for the solution of first order differential equations[edit | edit source]
The improved Euler formula[edit | edit source]
where
and
Second order differential equations[edit | edit source]
The AQA's free textbook [1]